Problem: Simplify the following expression: $k = \dfrac{8fh}{10fh + 8h} - \dfrac{2gh + 2h^2}{10fh + 8h}$ You can assume $f,g,h \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{8fh - (2gh + 2h^2)}{10fh + 8h}$ $k = \dfrac{8fh - 2gh - 2h^2}{10fh + 8h}$ The numerator and denominator have a common factor of $2h$, so we can simplify $k = \dfrac{4f - g - h}{5f + 4}$